Hi Tammie,

Instead of a trigger, you should go for Scheduled APEX. Triggers are fired only when a record is edited. When the expiration date reaches today, there will not be an edit on the record which will fire the trigger. Hence, you should use scheduled APEX (http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_scheduler.htm) so that the code is invoked everyday without an edit. Here's how:

1.) Write an apex class using below code. I wrote this sample code assuming asset__c is a custom object under contacts. You may have to change it a little based on your setup:

global class changeContactRole implements Schedulable {
   global void execute(SchedulableContext SC) {
      list<contact> contactsToUpdate = new list<contact>();
      list<asset__c> assetList = [select contact__c,contact__r.Role__c,License_Expiration_Date__c from asset__c where License_Expiration_Date__c = :date.today()];
      for(asset__c asset:assetList){
              contact con = new contact();
              con.Id = asset.contact__c;
              con.Role__c = 'Previous User';
              contactsToUpdate.add(con);
      }
      update contactsToUpdate;
   }
}

2.) Undet Setup | Develop | Apex Classes, click on "Schedule APEX". On the new apex job page, give the job a name, select changeContactRole as the apex class, select frequency as weekly and select all days of the week to run it. Also, select end date as some date far in the future, and a preferred time to run the apex job daily.

3.) To write a test class for this, please use this as reference: http://www.salesforce.com/us/developer/docs/apexcode/Content/apex_scheduler.htm

4.) If you want to test the code to check if it works as expected for you, create the same as a trigger and test it out by manually changing the expiration date of a test asset record to today:

trigger updateContactRole on Asset__c (after update,after insert) {
    list<account> updates = new list<account>();
    list<asset__c> assetList = [select account__c,account__r.Role__c,License_Expiration_Date__c from asset__c where License_Expiration_Date__c = :date.today()];
      for(asset__c asset:assetList){
              account con = new account();
              con.Id = asset.account__c;
              con.Role__c = 'Previous User';
              updates.add(con);
      }
      update updates;
}

If this answers your question, please mark this as the Best Answer for this post, so that others can benefit from this post.

Thanks,
Shashank